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MiS Preprint
63/1998

Light-cone expansion of the Dirac sea in the presence of chiral and scalar potentials

Felix Finster

Abstract

We study the Dirac sea in the presence of external chiral and scalar/pseudoscalar potentials. In preparation, a method is developed for calculating the advanced and retarded Green's functions in an expansion around the light cone. For this, we first expand all Feynman diagrams and then explicitly sum up the perturbation series. The light-cone expansion expresses the Green's functions as an infinite sum of line integrals over the external potential and its partial derivatives.

The Dirac sea is decomposed into a causal and a non-causal contribution. The causal contribution has a light-cone expansion which is closely related to the light-cone expansion of the Green's functions; it describes the singular behavior of the Dirac sea in terms of nested line integrals along the light cone. The non-causal contribution, on the other hand, is, to every order in perturbation theory, a smooth function in position space.

Received:
Jan 23, 1999
Published:
Jan 23, 1999

Related publications

inJournal
1999 Repository Open Access
Felix Finster

Light-cone expansion of the Dirac sea to first order in the external potential

In: The Michigan mathematical journal, 46 (1999) 2, pp. 377-408